Exercise 15 C
Question 1
Determine the mode for each of the following sets of data :
(a) 5,3,5,2,3,5,1,7
Ans: Mode 5
(b) 1,7,13,19,25
Ans: No mode
(c) 4,6,8,4,10,4,6,12,6,10
Ans: 4 and 6
(d) 51,68,70,76,76,55,70,73,68,70,81
Ans: 70
(e) 8,4,8,4,8,4,8,4,8,4,8,4
Ans: 4 and 8
(f) 29,29,10,10,3,3,14,10,2,2
Ans: 10
(g) 26,32,26,21,83,26,83,85
Ans: 26 and 83
Question 2
Find the mode of the following distributions:
(a)
$\begin{array}{|l|l|l|l|l|l|l|}\hline \text { Size } & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text { fre } & 4 & 6 & 2 & 5 & 3 & 1 \\\hline\end{array}$
Ans: Mode :3
(b)
$\begin{array}{|l|l|l|l|l|l|}\hline \begin{array}{l}\text { Size of } \\\text { shoes }\end{array} & 6 & 7 & 8 & 9 & 10 \\\hline \begin{array}{l}\text { No of } \\\text { person }\end{array} & 12 & 20 & 40 & 15 & 7 \\\hline\end{array}$
Ans: Mode : 8
Question 3
Determine (a) the mode (b) the median , and (c) the mean for each of the following sets of data:
(i) $1,16,11,6,11,8,14,11,21$
Sol: mode = 11
1,6,8,11,11,14,16,21
Median= 11
Mean $\bar{x}=\frac{Sum of observation}{No of observation}$
$=\frac{1+6+8+11+11+11+14+16+21}{9}$= $\frac{99}{9}=11$
(ii) $3,10,10,12,14,16,16,18,18,25$
Mode = 10,16 and 18
Sol: 3,10,10,12,14,16,18,18,25
Median = $\frac{14+16}{2}$
=$\frac{30}{2}=15$
Mean $\bar{x}=\frac{3+10+10+12+14+16+16+18+18+25}{10}$
=$\frac{142}{10}$ = 14.2
(iii) $23,2,42,6,36,11,29,9,15$
Mode = No mode
2,6,9,11,15,23,29,36,42
Median = 15
Mean
$\begin{aligned} \bar{x} &=\frac{2+6,+9+11+15+23+29+36+42}{9} \\ &=\frac{173}{9}=19 \frac{2}{9} \end{aligned}$
(iv) $8,8,8,8,18,18,18,18$
Sol: Mode = 8 and 18
8,8,8,8,18,18,18,18
Median = $\frac{8+18}{2}$
$=\frac{26}{2}=13$
$\operatorname{mean} \vec{x} =\frac{8,8,8,8,18,18,18,18}{8}$
$=\frac{104}{8}=13$
Question 4
Find the mode, and the mean for the set of data below.
Number of fiction books read by 28 eight grade pupils:
$4,6,1,7,3,9,5,7,8,5,4,6,10,6,9,5,6,6,8,6,8,5,10,7,2,5,3,7$.
Sol: Mode = 6
Mean = $=\frac{4+6+1+7+3+9+5+7+8+5+4+6+10+6+9+5+6+6+8+6+8+5+10+7+2+5+3+7}{28}$
$=\frac{168}{28}$ = 6
Question 5
Find the mode and the mean of the following set showing number of hours of operating life of 25 flashlight batteries:
$20,21,19,22,18,23,25,22,23,20,23,20,22,21,24,21,22,23,19,21,22,22,24,26,22 .$
Sol: Mode = 22
Mean = $\frac{545}{25}=21.8$
Question 6
Tell whether the statement is true or false:
(i) The mode is always one of the numbers in a data.- True
(ii) The mean is one of the numbers in a data - False
(iii) The median is always one of the numbers in a data- False
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